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For Albums, go to any album and select SAVE.

For Songs, select on any song.

For Artists, Podcasts, Videos, Radio stations, and Playlists, go to any and select FOLLOW.

Note: You can save a maximum of 10,000 songs and albums to Your Library. For albums, all its songs plus the album itself count towards the limit (e.g. a 10 track album counts as 11 tracks toward the limit). If your collection is so awesome you run out of room, you can always add songs to playlists.